*Disclaimer: this answer is based on a grammatical standard, which has been shown to be a "myth" in a response to a related question. I posted my answer here before reading the previous discussion on this whole issue of "less" versus "fewer". I would like to make it clear that my views are not based on some pretentious notions of superior knowledge of grammar. This is simply a standard I have always followed based on my background in English. I leave it to the reader to decide what they want to stick to. Thanks.
Indeed, one should use "fewer" for countable quantities. In fact, the usage of "less" for such quantities is grammatically incorrect. Also, I agree that a percentage is really a fraction. As such, it is apparently not a countable quantity in the grammatical sense. But, there's a catch! The word "percent" means "one part out of every hundred". Thus, if the percentage turns out to be countable, then one gets a countable quantity. When referring to a group of people, this is usually the case. Therefore, in your example sentence, the absolutely correct choice would be "fewer":
Fewer than 10.7% of the people were happy.
As the subject of the sentence "fewer than 10.7%" is certainly a countable quantity.
Now, for a counter example using cake! A fraction of a cake is not countable, no matter how you look at it. Thus, this example is correct:
Less than 10.7% of the cake was eaten.
(although 10.7% is a very arbitrary fraction to use for cake!)
In general, the rule* for percentages would be: